J. Phys. II France
Volume 7, Numéro 2, February 1997
Page(s) 249 - 255
DOI: 10.1051/jp2:1997122
J. Phys. II France 7 (1997) 249-255

Analytical Weak-Segregation Theory of Bicontinuous Phases in Diblock Copolymers

Scott T. Milner and Peter D. Olmsted

Exxon Research & Engineering Company, Corporate Research Science Laboratories, Annandale NJ 08801, USA

(Received 26 July 1996, received in final form 21 October 1996, accepted 7 November 1996)

We compute phase diagrams for diblock copolymers in the mean-field weak segregation regime as a function of the fraction f of A-monomers and the repulsive interaction $\chi N$. We include the ordered bicontinuous double-diamond (OBDD) phase [space group Pn3m] and the gyroid phase [space group Ia3d] as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and lamellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher [220] reflections in addition to the [211] fundamental. The gyroid free energy is favored by terms of the form $\psi_{[211]}^3 \psi_{[220]}$ and $\psi_{[211]}^2\psi_{[220]}$; the analogous terms are not permitted for OBDD.

© Les Editions de Physique 1997